Fault-tolerant control for Markov jump nonlinear systems based on an observer and finite-time fast integral terminal sliding mode control

This paper develops a novel fault-tolerant control based on an observer for underactuated robot manipulators with unknown external disturbances, uncertainties, and actuator faults. First, unlike the traditional approach of treating the robot system as a parameter time-varying system, the underactuated robot manipulator with different drive modes can be considered as one of the classical Markov jump nonlinear systems (MJNSs). Second, an adaptive disturbance observer is designed to estimate the state and disturbances of the system. Finally, based on the observation results, a nonsingular fast integral terminal sliding mode controller (NFITSMC) is utilized to implement fault-tolerant control of the system. Compared with traditional observer and terminal sliding mode controller, the adoption of the novel controller and observer can improve response time and reduce chattering. Especially, in order to eliminate chattering, the integral term is introduced into the nonsingular fast terminal sliding mode controller. Structuring Lyapunov–Krasovskii functional (LKF) and based on linear matrix inequalities (LMIs) techniques, the convergence of control strategy and tracking errors is proved. The simulation results show that the actuator faults can be observed successfully and the error system is finite-time stable.